Let 9t and be commutative rings such that contains, and has the same identity element as, 9. If p and are prime ideals in SK and respectively such that P\9t = p then we shall say that lies over, or contracts to, p. If over every prime ideal in dt there lies a prime ideal in , we shall say that the "lying-over" theorem holds for the pair of rings 9 and .
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Cohen et al. (1946) studied this question.